Evolution dynamics of spinning binaries in effective-one-body theory to fifth Post-Minkowskian order

This paper investigates a self-consistent effective-one-body (EOB) theory developed to describe the dynamics of spinning binary systems. We systematically derive, using field-theoretic principles, all expressions and quantities entering Hamilton's equations, which govern the dynamical evolution of the system. Based on the effective rotating metric up to fifth post-Minkowskian (PM) order recently obtained by us, we construct the Hamiltonian and the stress-energy tensor. We then derive a decoupled, separable Teukolsky-like equation with a source term for the Newman--Penrose Weyl scalar $ψ_4^B$ and present its formal solution. Finally, using this solution, we obtain the energy flux, radiation-reaction force, and gravitational waveforms for the ``plus'' and ``cross'' polarizations generated by spinning binaries. The EOB theory applies to systems with arbitrary mass ratio, which filling the gap between comparable mass ratios and extreme mass ratios.